Wednesday, September 21, 2016

Physics is usually associated with frying the brain rather than saving it. Unfortunately, students often leave introductory physics classes wondering more about the relevance of physics than the world of possibilities it opens. Whatever you wonder about, one thing is clear. The part of you that does the wondering is fundamental to who you are.

As complex and mysterious as the brain may be, it’s still subject to the laws of physics. Knowing how the brain behaves at its most vulnerable is key to keeping it safe and helping it heal after trauma. This is the subject of new research by scientists from the University of Oxford and Stanford University that was published today in the journal Physical Review Letters.

When a stroke, tumor, or injury causes intense swelling in the brain, the pressure can rise so high that it restricts blood flow. This can have lasting and even fatal consequences. As a last resort, surgeons sometimes perform a decompressive craniectomy to relieve the pressure, a procedure in which they remove a piece of the skull so that the brain can swell outward. The piece is replaced after the swelling goes down.

A simulation for 10% brain swelling after a decompressive craniectomy.
Areas of high shear stress are circled. Inset: A transverse section showing
radial fiber stretch. The area of high radial stretch is circled.Image Credit: Alan Goriely, Johannes Weickenmeier, and Ellen Kuhl/PRL

This procedure has been used for more than a century, but its success rate is far less than ideal and the risk of damage is high. For example, if the opening is too small, the bulge could herniate or compress the veins around the edges in way that inhibits blood supply. A craniectomy can also cause the axons (the long part of the neurons) to stretch and sometimes die.

The thing is, exactly what happens to the shape of the brain during and after a craniectomy is not well understood. The key question the research team asked is this: When one part of the brain bulges through the opening, how is the rest of the brain affected? In other words, does this process lead to deformations that could damage other areas of the brain? If so, where?

Researchers Alain Goriely, Ellen Kuhl, and Johannes Weickenmeier started by turning this high-stakes clinical problem into a more generic physical problem. It turns out that from a physics point of view, you can learn a lot by ignoring the mysteries of the brain and thinking about it as simply a soft solid.

Imagine that you have a soft solid constrained except for one circular hole through which it can expand. As the solid swells, what is the shape of the bulge? What stresses and stretches does this create in different areas of the solid? The researchers aimed to solve these questions theoretically, and then apply the solutions to the specific case of the brain.

Putting their math skills to work, the team started from basic physics theory and found the relationships between the size of the hole, the shape of the bulge, and the stresses and stretches experienced by different parts of the solid. Their mathematical model showed areas of increasingly high stress around the opening. They showed a significant amount of stretching in the center of the bulge, and of compression at the edges.

In order to be sure that their physical model was accurate, the team tested their idealized mathematical model against a precise numerical simulation of the same problem. The simulation revealed these same findings, even for more complicated geometries.

To more closely explore the possible impacts of a craniectomy, the researchers considered the problem of swelling in an anatomically correct geometry based on high-resolution brain and skull scans. Again, they saw very high stresses around the opening and the same areas of high stretching that were predicted by the simple model. These may correlate to the two most well-known types of damage caused by craniectomies, herniation and damage to the axons caused by stretching.

In the search for the most effective, lowest-risk treatment for swelling in the brain, the next step is to combine this theoretical research with experiments and clinical work. This study is part of the large, interdisciplinary research program of the International Brain Mechanics and Trauma Lab. The lab seeks to understand the physics of the brain and how it impacts functions. Hopefully by bringing together experts in math, physics, biology, neuroscience, medicine, and other fields, we will soon be able to care for these complex, mysterious structures in a more informed way.